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Colon, :, HColon

Syntax

Colon(M:IDEAL,N:IDEAL):IDEAL
Colon(M:MODULE,N:MODULE):IDEAL
M : N
HColon(M:IDEAL,N:IDEAL):IDEAL
    

Summary

ideal or module quotient

Description

These functions return the quotient of M by N: the ideal of polynomials F in R such that FG is in M for all G in N. The command M : N is a shortcut for Colon(M,N).

The function HColon calculates the ideal quotient using a Hilbert-driven algorithm. It differs from Colon only when the input is inhomogeneous, in which case, HColon may be faster.

example

    
Use R ::= Q[x,y];
Ideal(xy,x^2) : Ideal(x);
Ideal(y, x)
-------------------------------
Colon(Ideal(x^2,xy),Ideal(x,x-y^2));
Ideal(x)
-------------------------------
HColon(Ideal(x^2,xy),Ideal(x,x-y^2));
Ideal(x)
-------------------------------
        
    

See Also